connect the centers of the three smaller circles, which forms an equilateral triangle with side length .

height of this equilateral triangle (which is also a median) is

the centroid of the equilateral triangle is the center of the large circle ... you need to calculate the distance along the median from the triangle's vertex to the centroid, and add that distance to to get the large circle's radius.

recall the ratio that a centroid divides a median.